Boundary and Interior Layers, Computational and Asymptotic by Petr Knobloch PDF
By Petr Knobloch
This quantity bargains contributions reflecting a variety of the lectures offered on the overseas convention BAIL 2014, which was once held from fifteenth to nineteenth September 2014 on the Charles college in Prague, Czech Republic. those are dedicated to the theoretical and/or numerical research of difficulties concerning boundary and inside layers and techniques for fixing those difficulties numerically. The authors are either mathematicians (pure and utilized) and engineers, and convey jointly numerous attention-grabbing principles. the big variety of issues handled within the contributions presents an outstanding evaluation of present learn into the speculation and numerical answer of difficulties related to boundary and inside layers.
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This quantity bargains contributions reflecting a range of the lectures awarded on the foreign convention BAIL 2014, which was once held from fifteenth to nineteenth September 2014 on the Charles collage in Prague, Czech Republic. those are dedicated to the theoretical and/or numerical research of difficulties related to boundary and inside layers and strategies for fixing those difficulties numerically.
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Extra info for Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014
However, not even existence of weak solutions can be shown, if this condition is used for the Navier-Stokes equation, see . The reason is that this boundary condition does not exhibit any control about inflow across such boundaries, see . This has also severe impact onto the stability of numerical algorithms for flows at higher Reynolds numbers. The directional do-nothing (DDN) boundary condition is one possibility to circumvent this disadvantage. g. [1, 7]. The issue of appropriate boundary conditions for the Navier-Stokes and Euler system is also recently addressed by Becker et al.
0; 1/2 be the unit square and let K D I, with > 0. x; y/ 2 ˝ ; (31) and v D K rp. 1; 1/. RT 0 ; L1 / with uniform refinement (FEM algorithm) and the adaptive refinement algorithm (AFEM) described above. We choose Ä1 D 2 and Ä2 D 1:0. We remark that these values of the stabilization parameters are consistent with the theory and ensure that the bilinear form As . ; / is elliptic in the whole space. For implementation purposes, instead of imposing the null media condition required to the elements of Mh , we fix to zero the value of the pressure in a corner of the domain.
Layers, as this requires very fine meshes in the normal direction to the wall (see, for instance, John and Kindl , Bazilevs et al. ). A way to overcome this difficulty, recently applied to VMS models, is to weakly impose no-slip boundary conditions (cf. [4, 5]), that consistently incorporate the “law of the wall” in a weak sense. However, this requires to solve the flow in the whole physical domain (the advantage is the use of uniform meshes vs. stretched meshes, but there is no reduction in number of degrees of freedom).
Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014 by Petr Knobloch